The solenoid ON the starter motor does need to be activated using its smaller "S" connection or the gear won't engage the flywheel/ring gear
There are some "terms" that are confusing
The electrical connection on the inner fender was called the "starter solenoid" for years, it was always the "starter RELAY" but not what it was called
The smaller cylinder on the starter motor is a "solenoid", but ALSO a relay it does both functions
It moves the gear out, and also connects starter motor to larger battery cable
Starter relay seen here:
https://i.ytimg.com/vi/WetjBauPgrY/maxresdefault.jpg
Starter solenoid/relay seen here:
https://infinitybox.com/wp-content/uploads/2016/06/starterterm.jpg
The "S" post gets 12v when key is turned to START(from the starter relay), this moves starter gear OUT and connects Battery Positive directly to starter motor
If starter motor just gets 12v then it would only spin, "S" post must also get 12v, and FIRST
100+ years ago the term "solenoid" was given to any device that moved a metal rod inside a coil of wire when that coil of wire was powered
A "relay" uses the same coil and movement of the rod, so it IS a solenoid, but...................
There needed to be a different designation because they do different things
A Relay is used to make and break electrical connections
A Solenoid is used to cause movement
So Ford starter motor has a dual unit on top of it, it MOVES the starter gear, and it MAKES an electrical connection
The unit in the fuse box or on inner fender is a RELAY, it MAKES an electrical connection ONLY
Some argue that movement of relay's "bar" to make the connection means its a solenoid, and 70 years ago they would be in the majority, although still WRONG, lol
Use of the terms "relay" and "solenoid" is in its main function, Electric connection or Movement
Modern automatic transmission have several "solenoids" and they are called that because they MOVE valves in the valve body
And vehicles have many "relays" to activate electrical circuits, it would be incorrect to call them "solenoids", so also incorrect to call inner fender starter relay a starter solenoid, because it ain't one